If the money is saved in a bank or invested, it is loaned out then spent - tracked in the GDP figures.
If the money is saved in a mattress, this would effectively decrease the money supply, lowering the price level (if people did this en masse) where producers would eventually renegotiate prices at this lower price level and push the GDP back out to the long run.
If the money is saved in a mattress, this would effectively decrease the money supply, lowering the price level (if people did this en masse) where producers would eventually renegotiate prices at this lower price level and push the GDP back out to the long run.